- #1

hogrampage

- 108

- 1

## Homework Statement

Find V

_{L}(t) and V

_{c}(t) in the circuit below

Where V

_{s}= cos(200[itex]\pi[/itex]t) V

## Homework Equations

[itex]\alpha[/itex] = [itex]\frac{1}{2RC}[/itex]

ω

_{0}= [itex]\frac{1}{\sqrt{LC}}[/itex]

[itex]\omega[/itex]

_{0}= [itex]\sqrt{\omega^{2}-\alpha^{2}}[/itex]

## The Attempt at a Solution

Well, I found the total capacitance

C = 1.5 uF

Then, I found [itex]\alpha[/itex]:

[itex]\alpha[/itex] = [itex]\frac{1}{2(100Ω)(1.5uF)}[/itex] ≈ 3333 s

^{-1}

and

ω

_{0}= [itex]\frac{1}{\sqrt{(20mH)(1.5uF)}}[/itex] ≈ 5774 s

^{-1}

So V

_{c}= B

_{1}e

^{-3333}cos([itex]5774\pi[/itex]t) + B

_{2}e

^{-3333}sin([itex]5774\pi[/itex]t)

That's as far as I went. I have no idea what I'm doing :|. Also, please note that I have NOT had differential equations. This class does not require it, so please give an answer without using DQ's.